A tube-filling and boxing machine must be supplied from a supply hopper in which the horizontally disposed tubes are stored, in individual succession and in a positive manner with these tubes, to supply them so that they are in a vertical arrangement with their open bases facing upwardly resiliently acting take-up members of the processing line along which the tubes are moved in successive steps and are filled and have their bases sealed in a conventional manner. The tubes processed in this way, i.e. filled and with their bases sealed, are taken up, still in phase with the successive step feed along the processing line, rhythmically, by transfer members designed to insert them in respective prefabricated packaging boxes or containers having their filling apertures upwardly open, which members are displaced, still in a positive manner, in an identical rhythmic succession to a boxing station and are closed at this station inside the corresponding boxes with the subsequent closure of the filling aperture.